“In today’s lesson, we are going to use multiplication to solve word problems. First, let’s make a list of key words or phrases that are related to the concept of multiplication. These will be like clues, helping us to know when to use multiplication. Now, can anyone think of some words or phrases that might be telling us to multiply?”
Allow students to brainstorm and call out key words or phrases as you write their suggestions on the board or overhead. (Some examples include times, per, each, every, product.)
“We are going to look at a few examples of word problems that require multiplication. Remember, when we see words from the list we created in a problem, it might be a clue telling us to use multiplication!”
Present the following word problem.
- At the amusement park, Kelly bought three strips of tickets. Each strip had four tickets. How many tickets did Kelly have?
“First of all, what are the ‘clues’ in the problem that indicate we need to multiply?” (the word “each”)
“Work with your neighbor to generate two different ways of solving this problem.”
Give students a few minutes to develop two different solution methods. When they are finished, ask for volunteers to share their methods and record them on chart paper. Methods can include repeated addition (4 + 4 + 4 = 12); skip counting by 4s (4, 8, 12); writing a multiplication equation (3 × 4 = 12); and modeling using a manipulative (counters, chips) and then counting up the total.
“These are all good methods, and it is important to understand them all, but right now we are going to focus on writing multiplication equations.”
Give each student a dry-erase board. Present the following problems to students. For each problem, ask them to write a multiplication number sentence for the word problem on their dry-erase boards and hold the boards up. Remind students that when writing a number sentence for a multiplication problem, they need to use a multiplication symbol and an equal sign.
- The man selling cotton candy had five pink-colored bags. There were four times as many green-colored bags as pink. How many green-colored bags of cotton candy did the man have to sell?
- The man selling cotton candy had 15 bags of cotton candy to sell. Each bag cost $3 and he sold all the bags. How much money did he receive?
- There were five roller coasters at the amusement park. There were six times as many children’s rides as roller coasters. How many children’s rides were there?
“Can someone summarize how you know when to use multiplication to solve a word problem? What clues help you?” (the key words)
“Now, see if you can create your own multiplication word problem. If we stick with the topic of an amusement park, can you create a word problem that would require multiplication? Think about the people, rides, games, food, tickets, and souvenir shops you might see at an amusement park. Take a few moments with the people around you and see if you can write a word problem that would require multiplication. Then record your problem on chart paper.”
Ask volunteers to share their problems. As a class, discuss if each example is indeed a word problem that requires multiplication. If so, ask students to write the corresponding multiplication number sentence necessary for solving. These problems, if authentic, can be used throughout the unit as review.
“A moment ago, we practiced solving multiplication word problems by writing multiplication equations. Now, we are going to talk about some different strategies using base-ten blocks. Let’s do an example together.”
Present the following problem.
- An amusement park ride has 12 cars. Each car can carry three people. How many people can the ride carry?
Provide the students with base-ten blocks. Encourage students to use the blocks (in more than one way) to solve the problem. Then have students record the process they used, along with number sentences for the solutions. Ask students to share their solutions. Two possible strategies might include making groups of three cubes and then counting up by threes 12 times or making a list of 12 threes to add (repeated addition). Other students might think (6 × 3) + (6 × 3). Students break apart products into the sum of simpler products using multiplication facts they know. Students may not know 12 × 3, but they know they can break 12 into two groups of 6. Another approach might be to break apart, or decompose, 12 to (10 + 2) and think (10 × 3) + (2 × 3).
As students discuss their strategies, point out how in each solution there are 10 groups of 3, with 2 extra groups of 3 that need to be added on. Record the following number sentence for students to see: (10 × 3) + (2 × 3) = 36.
“Is the equation true or false? (10 × 3) + (2 × 3) = 12 × 3. Why?” (True. Both sides of the equation equal 36.) “What is another number sentence that is the same as 12 × 3?” Guide students to realize that any way of breaking up the 12 into a sum of two addends and multiplying each addend by 3 would work. (Some examples include (9 × 3) + (3 × 3), (8 × 3) + (4 × 3), etc.)
Provide additional problems based on the amusement park context.
- An amusement park ride has seats arranged in long rows. There are 12 seats in each row. There are four rows. How many children can ride?
- Tickets for the rides are bought in books of 15 tickets per book. There are five children who want to ride the rides. An adult bought five books so each child could have one book. How many tickets did the adult buy in total?
- Karl took three rides before lunch and five times as many rides after lunch. How many rides did Karl take in total?
- One game at the amusement park cost $0.25. Karl wanted to play the game three times. How much would it cost to play three times?
“For each word problem, identify the key words that indicate multiplication and then write three equal multiplication equations that could be used.” Monitor performance and explanations. Post some of the strategies that students use on chart paper and have students discuss the similarities between the strategies. Encourage students to try decomposing numbers to solve the multiplication problems. For example, use the above problems: 12 4 = (10 × 4) + (2 × 4) and 15 × 5 = (10 × 5) + (5 × 5), etc.
Station Rotation
Set up three work stations for students. Station 1 will provide word problems that focus on equation writing. Station 2 will offer students an opportunity to practice writing word problems. Station 3 will focus on writing numbers in expanded notation (distributive property over addition).While students are working at each station, monitor student progress. Provide necessary interventions and support as needed. Keep track of student understanding on the Observation Checklist (M-4-2-1_Observation Checklist.docx).
Station 1: Writing Equations
Provide the following word problems for Station 1. Ask students to use different strategies to solve the problems and create as many varied equations as they can to solve the problems. Use the first word problem below to model that equations have equal signs.
- In a package of chocolate chip cookies, Alice counted 15 cookies in each row and there were three rows in the package. How many chocolate chip cookies were in the package?
- 3 × 15 = 15 + 15 + 15 = ____.
- On the classroom bookshelf, students counted eight mysteries. There were three times as many realistic fiction books as mysteries. How many realistic fiction books were on the classroom bookshelf?
- A farmer planted 16 rows of tomatoes. The farmer planted five tomato plants in each row. How many tomato plants did the farmer plant?
Station 2: Writing Multiplication Word Problems
For Station 2, students will use the Word Problem Template (M-4-2-1_Word Problem Template.docx) to create two different word problems that require multiplication to solve. Ask them to show at least two strategies they could use to solve each problem.
Station 3: Writing Numbers in Expanded Notation (Distributive Property over Addition)
For Station 3, provide the following number sentences and ask students to explain if the sentences are true or false and how they know.
- (10 × 4) + (3 × 4) = 13 × 4
- 24 × 4 = (20 × 2) + (4 × 2)
- 18 × 6 = (10 × 6) + (8 × 6)
Use base-ten blocks to model a multiplication problem. Ask students to write the number sentence that matches the model on a dry-erase board and hold it up. Repeat by modeling two or three other examples for students. Then have students explain to a partner how they would solve a problem like 14 × 5. Observe and listen to students to monitor for understanding. Correct any misunderstandings.
Ask students to solve 18 ×7 as a journal response. Then have students explain what they did and why they did each step. Finally ask students to explain why they used the strategy they did to solve the problem.
Extension:
- Routine: Write a two-digit by one-digit multiplication problem on the board. Have students individually think about, then write down, two different ways to represent the problem. Pair students up and have the partners share representations. Discuss the results. This think-pair-share activity can be used as a warm-up at the beginning of another class session or as an exit ticket for this lesson.
- Expansion: Have students make a poster showing different ways of solving one-digit by two-digit multiplication problems. They can put each strategy into its own column and title it. Or have students who have mastered the concepts explain strategies to students who need assistance.
Students can also use the technique of writing in expanded notation to solve a multiplication problem: 18 × 6 = (10 × 6) + (10 × 6) − (2 × 6). Ask students if they can explain why this works. Breaking apart 18 into 10s can help in solving this problem. One group of 10 is not enough; 2 groups of 10 are too much. Students should see that instead of using 18 groups of 6 as the original problem states, estimation is used. Since the number of groups is overestimated by 2, the two extra groups of 6 have to be subtracted. Once students are able to explain why this method works, have them try to create other multiplication problems where this method can be used. Students can then exchange multiplication problems with a partner and try to solve the problems using expanded notation.
- Small Group: Use the Multiplication Practice worksheet (M-4-2-1_Multiplication Practice.docx). This worksheet has been created specifically for small-groups of students.
- Technology Connection: Have students practice two-digit multiplication with the Rags-to-Riches game. In this game, the focus is on tens and on place value. Students practice their multiplication skills and get results immediately. See Rags-to-Riches at http://www.quia.com/rr/10206.html.
